Objectif Our field is cryptology. Our overarching objective is to advance significantly the frontiers indesign and analysis of high-security cryptography for the future generation. Particularly, we wish to enhance the efficiency, functionality, and, last-but-not-least, fundamental understanding of cryptographic security against very powerful adversaries.Our approach here is to develop completely novel methods by deepening, strengthening and broadening the algebraic foundations of the field.Concretely, our lens builds onthe arithmetic codex. This is a general, abstract cryptographic primitive whose basic theory we recently developed and whose asymptotic part, which relies on algebraic geometry, enjoys crucial applications in surprising foundational results on constant communication-rate two-party cryptography. A codex is a linear (error correcting) code that, when endowing its ambient vector space just with coordinate-wise multiplication, can be viewed as simulating, up to some degree, richer arithmetical structures such as finite fields (or products thereof), or generally, finite-dimensional algebras over finite fields. Besides this degree, coordinate-localities for which simulation holds and for which it does not at all are also captured.Our method is based on novel perspectives on codices which significantly widen their scope and strengthen their utility. Particularly, we bring symmetries, computational- and complexity theoretic aspects, and connections with algebraic number theory, -geometry, and -combinatorics into play in novel ways. Our applications range from public-key cryptography to secure multi-party computation.Our proposal is subdivided into 3 interconnected modules:(1) Algebraic- and Number Theoretical Cryptanalysis(2) Construction of Algebraic Crypto Primitives(3) Advanced Theory of Arithmetic Codices Champ scientifique natural sciencescomputer and information sciencescomputer securitycryptographynatural sciencesmathematicspure mathematicsarithmeticsnatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsdiscrete mathematicscombinatoricsnatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Mots‑clés cryptology public key cryptography secure computation algebraic methods Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Thème(s) ERC-2016-ADG - ERC Advanced Grant Appel à propositions ERC-2016-ADG Voir d’autres projets de cet appel Régime de financement ERC-ADG - Advanced Grant Institution d’accueil STICHTING NEDERLANDSE WETENSCHAPPELIJK ONDERZOEK INSTITUTEN Contribution nette de l'UE € 2 447 439,00 Adresse WINTHONTLAAN 2 3526 KV Utrecht Pays-Bas Voir sur la carte Région West-Nederland Utrecht Utrecht Type d’activité Research Organisations Liens Contacter l’organisation Opens in new window Site web Opens in new window Participation aux programmes de R&I de l'UE Opens in new window Réseau de collaboration HORIZON Opens in new window Coût total € 2 447 439,00 Bénéficiaires (1) Trier par ordre alphabétique Trier par contribution nette de l'UE Tout développer Tout réduire STICHTING NEDERLANDSE WETENSCHAPPELIJK ONDERZOEK INSTITUTEN Pays-Bas Contribution nette de l'UE € 2 447 439,00 Adresse WINTHONTLAAN 2 3526 KV Utrecht Voir sur la carte Région West-Nederland Utrecht Utrecht Type d’activité Research Organisations Liens Contacter l’organisation Opens in new window Site web Opens in new window Participation aux programmes de R&I de l'UE Opens in new window Réseau de collaboration HORIZON Opens in new window Coût total € 2 447 439,00